Game with Two Trees

The Smart Beaver from ABBYY has come up with a new developing game for children. The Beaver thinks that this game will help children to understand programming better.

The main object of the game is finite rooted trees, each of their edges contains some lowercase English letter. Vertices on any tree are always numbered sequentially from 1 to m, where m is the number of vertices in the tree. Before describing the actual game, let's introduce some definitions.

We'll assume that the sequence of vertices with numbers v₁, v₂, ..., v_k (k ≥ 1) is a forward path, if for any integer i from 1 to k - 1 vertex v_i is a direct ancestor of vertex v_i + 1. If we sequentially write out all letters from the the edges of the given path from v₁ to v_k, we get some string (k = 1 gives us an empty string). We'll say that such string corresponds to forward path v₁, v₂, ..., v_k.

We'll assume that the sequence of tree vertices with numbers v₁, v₂, ..., v_k (k ≥ 1) is a backward path if for any integer i from 1 to k - 1 vertex v_i is the direct descendant of vertex v_i + 1. If we sequentially write out all the letters from the edges of the given path from v₁ to v_k, we get some string (k = 1 gives us an empty string). We'll say that such string corresponds to backward path v₁, v₂, ..., v_k.

Now let's describe the game that the Smart Beaver from ABBYY has come up with. The game uses two rooted trees, each of which initially consists of one vertex with number 1. The player is given some sequence of operations. Each operation is characterized by three values (t, v, c) where:

• t is the number of the tree on which the operation is executed (1 or 2);
• v is the vertex index in this tree (it is guaranteed that the tree contains a vertex with this index);
• c is a lowercase English letter.

The actual operation is as follows: vertex v of tree t gets a new descendant with number m + 1 (where m is the current number of vertices in tree t), and there should be letter c put on the new edge from vertex v to vertex m + 1.

We'll say that an ordered group of three integers (i, j, q) is a good combination if:

• 1 ≤ i ≤ m₁, where m₁ is the number of vertices in the first tree;
• 1 ≤ j, q ≤ m₂, where m₂ is the number of vertices in the second tree;
• there exists a forward path v₁, v₂, ..., v_k such that v₁ = j and v_k = q in the second tree;
• the string that corresponds to the forward path in the second tree from vertex j to vertex q equals the string that corresponds to the backward path in the first tree from vertex i to vertex 1 (note that both paths are determined uniquely).

Your task is to calculate the number of existing good combinations after each operation on the trees.